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A constituency consists of two parties A and B. A has a solid vote bank of 30% and B has a vote bank of x%. Remaining parties are neutral voters. Out of the neutral voters, a section of them turn up for the election and 60% of those who turned voted for A. Out of others who didn’t vote 70% of them have voted for B. Originally A got 28 4/7% more votes than B. But if the people who did not turn up voted, A would have still won but by 4 4/49%. What is the percentage amount of voters who did not vote?

A constituency consists of two parties A and B. A has a solid vote bank of 30% and B has a vote bank of x%. Remaining parties are neutral voters. Out of the neutral voters, a section of them turn up for the election and 60% of those who turned voted for A. Out of others who didn’t vote 70% of them have voted for B. Originally A got 28 4/7% more votes than B. But if the people who did not turn up voted, A would have still won but by 4 4/49%. What is the percentage amount of voters who did not vote? Correct Answer 20

30% people vote A (not neutral voters)

x% for B

So, % amount of neutral voters = 100 – 30 – x = 70 – x

Let y% of total people be the percentage amount of neutral voters who came for the election.

Total vote for A = 30 + 60/100 × y = 30 + 0.6y

Total vote for B = x + 40/100 × y = x + 0.4y

Given Total vote for A = 28 4/7% = 200/7% more than B

⇒ 30 + 0.6y = (100 + 200/7) /100 × (x + 0.4y)

⇒ 30 + 0.6y = 9/7 × (x + 0.4y)

⇒ 210 + 4.2y = 9x + 3.6y

∴ 9x = 210 + 0.6y       ----1

Now amount of neutral voters who didn’t vote = 70 – x – y

If they voted

Total vote for A = 30 + 60/100 × y + 30/100 × (70 – x – y)

⇒ 51 + 0.3y – 0.3x

Total vote for B = x + 40/100 × y + 70/100 × (70 – x – y)

⇒ 49 + 0.3x – 0.3y

Total vote for A = 4 4/49% (200/49) more than B

51 + 0.3y – 0.3x = (100 + 200/49) /100 × (49 + 0.3x – 0.3y)

⇒ 51 + 0.3y – 0.3x = 51/49 × (49 + 0.3x – 0.3y)

⇒ 51 × 49 + 49 × 0.3 × (y – x) = 51 × 49 + 51 × 0.3 × (x – y)

⇒ 49 × 0.3 × (y – x) = 51 × 0.3 × (x – y)

This happens only when x = y

Substituting in Equation 1

9x = 210 + 0.6x

⇒ 8.4x = 210

So, x = y = 210/8.4

⇒ 25%

∴ Percentage amount of voters who didn’t vote = 70 – x – y = 20%

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